The algorithmic structure was examined of the vectorizable Stanford particle simulation (SPS) method and the structure is reformulated in data parallel form. Some of the SPS algorithms can be directly translated to data parallel, but several of the vectorizable algorithms have no direct data parallel equivalent. This requires the development of new, strictly data parallel algorithms. In particular, a new sorting algorithm is developed to identify collision candidates in the simulation and a master/slave algorithm is developed to minimize communication cost in large table look up. Validation of the method is undertaken through test calculations for thermal relaxation of a gas, shock wave profiles, and shock reflection from a stationary wall. A qualitative measure is provided of the performance of the Connection Machine for direct particle simulation. The massively parallel architecture of the Connection Machine is found quite suitable for this type of calculation. However, there are difficulties in taking full advantage of this architecture because of lack of a broad based tradition of data parallel programming. An important outcome of this work has been new data parallel algorithms specifically of use for direct particle simulation but which also expand the data parallel diction.